# Pedal power

Competitive cyclists have power meters to carefully monitor their training and race performance. Power is a measure of how much energy is being changed every second. For cyclists, the effort they put into pedalling either makes them go faster (extra kinetic energy – related to speed) or helps them fight against drag and rolling resistance. Any improvements to aerodynamic drag need to be weighed up against the amount of power that a cyclist can still produce if they need to use a different position.

## How much power can a cyclist produce?

Power is the best indicator of how well a cyclist will perform in terms of maximising their speed. An elite cyclist can produce about 5 watts (5W) of power for every kilogram of bodyweight for a 1-hour event. For example, a 70 kg cyclist who is able to maintain a power output of 350W for 1 hour would be considered to be in the elite category.

A very powerful cyclist might be able to produce 1200W or more for a few seconds. This is useful to make sure they reach maximum speed as soon as possible. In a team pursuit event, the most powerful cyclist is placed at the front for the start of a race to make sure the team reaches maximum speed quickly. For four cyclists riding in a close line, the second cyclist uses about 74% of the power of the lead cyclist. The third and fourth cyclists use about 64% of the power of the lead cyclist.

## How pedalling power relates to force and speed

The power of a cyclist depends on:

how much force the pedals are being pushed with

the speed at which the pedals are being turned around.

The maximum power occurs when the force pushing on the pedals multiplied by the speed of the pedals is greatest.

For example, if the cyclist applies a force of 150 newtons to the pedals (150N is the force needed to lift a 15kg mass) and the speed of the pedals in a circle is 2 metres per second (2m/s), the pedalling power output of the cyclist is:

Pedalling power = force on pedals x speed of pedals = 150N x 2m/s = 300W

This is the same power as lifting a 30kg mass upwards a height of 1 metre every second.

Power is a measure of how quickly energy is being changed into other forms. To understand why power is force multiplied by speed. There are two main ideas:

Change in energy is equal to the work done, which is force applied multiplied by distance moved.

Speed equals distance moved divided by time taken.

power = change in energy/time taken = work done/time = force x distance/time = force x speed

## Power can be used to calculate forwards force

The forwards force acting on the bike is not the same as the force pushing on the pedals. Assuming negligible energy losses, the forwards force on the cyclist is calculated as the pedalling power divided by the speed of the bike:

For example, if the power at the pedals is 300 watts (300W) and the speed of the bike is 40 kilometres per hour (40km/h = 11m/s), then the forwards force acting on the cyclist is:

Forwards force = pedalling power ÷ speed of bike = 300W ÷ 11m/s = 27N

## Faster speeds require more power to counter aerodynamic drag

To calculate the force and power needed to counter aerodynamic drag and rolling resistance at different speeds, the following equations can be used:

FD = ½CD AρV2 PD = ½CD AρV3

FD is the drag force.

PD is the power needed to counter drag.

CD is the drag coefficient (a number from about 0.5 to 1.1 for a cyclist, depending on bike, body position and equipment).

A is the frontal area of the object (measured in square metres). CDA is often grouped together as a term called the effective frontal area – normally between 0.4 and 0.7m2.

ρ is the density of air (about 1.2 kg/m3).

V is the speed the object is travelling at (measured in metres per second – m/s).

These equations can be used to show that, if speed increases by 10%, the force of aerodynamic drag increases by 21%, but the power (effort needed by the cyclist) increases by 33%.

To calculate the force and power needed to counter rolling resistance at different speeds, the following equations can be used:

FRR = CRR x m x g PRR = FRR x V

FRR is the rolling resistance force.

PRR is the power needed to counter rolling resistance.

CRR is the coefficient of rolling resistance (typically between 0.003 and 0.008 depending on tyres and the road surface). A higher number indicates more resistance.

m is the mass of the rider plus bike (measured in kilograms – kg).

g = 9.8 (multiplying mass by 9.8 gives the weight, which is the force downwards due to gravity

V is the speed the object is travelling at (measured in metres per second – m/s).

Even though the force of rolling resistance doesn’t change as speed increases, the power needed to work against rolling resistance increases. As you travel faster, there is more energy being converted into heat energy each second, so this requires more effort from the rider.

### Power needed to counter aerodynamic drag and rolling resistance

This graph shows the power needed for a typical cyclist to overcome aerodynamic drag and rolling resistance. Power needed to counter aerodynamic drag increases dramatically with speed.

**Rights:**The University of Waikato Te Whare Wānanga o Waikato

## Activity idea

In the Individual pursuit graphs activity, students cut out and tape different shapes, attach tiny pieces of cotton thread and use hairdryers to find which shape has the least drag. The shape that keeps airflow attached for longer reduces the low-pressure zone at the back, so it will have least drag.

**Published:**22 February 2011